Many information processing systems are configured to replicate data from a storage system at one site to a storage system at another site. In some cases, such arrangements are utilized to support disaster recovery functionality within the information processing system. For example, an enterprise may replicate data from a production data center to a disaster recovery data center. In the event of a disaster at the production site, applications can be started at the disaster recovery site using the data that has been replicated to that site so that the enterprise can continue its business. Data replication in these and other contexts can be implemented using asynchronous replication. For example, asynchronous replication may be configured to periodically transfer data in multiple cycles from a source site to a target site. Conventional approaches to data replication are problematic in that under certain circumstances, a given replication process can consume excessive amounts of bandwidth on network connections between the source and target sites, and additionally or alternatively can consume excessive computational resources on at least one of the source site and the target site, thereby undermining the efficiency of the replication process. This can in turn make it difficult to achieve a desired recover point objective within the information processing system.